On outindependent subgraphs of strongly regular graphs

An outindependent subgraph of a graph G, with respect to an independent vertex subset C¿¿V, is the subgraph GC induced by the vertices in V\¿C. We study the case when G is strongly regular, where the results of de Caen [1998, The spectra of complementary subgraphs in a strongly regular graph. Europe...

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Detalhes bibliográficos
Autores: Fiol Mora, Miquel Àngel|||0000-0003-1337-4952, Garriga Valle, Ernest
Formato: artículo
Fecha de publicación:2006
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/126902
Acesso em linha:https://hdl.handle.net/2117/126902
Access Level:acceso abierto
Palavra-chave:Combinatorial analysis
Graph theory
Strongly regular graph
Independent set
Spectrum
Combinacions (Matemàtica)
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Descrição
Resumo:An outindependent subgraph of a graph G, with respect to an independent vertex subset C¿¿V, is the subgraph GC induced by the vertices in V\¿C. We study the case when G is strongly regular, where the results of de Caen [1998, The spectra of complementary subgraphs in a strongly regular graph. European Journal of Combinatorics, 19 (5), 559–565.], allow us to derive the whole spectrum of GC . Moreover, when C attains the Hoffman–Lovász bound for the independence number, GC is a regular graph (in fact, distance-regular if G is a Moore graph). This article is mainly devoted to study the non-regular case. As a main result, we characterize the structure of GC when C is the neighborhood of either one vertex or one edge.